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Chaotic Inflation in No-Scale Supergravity with String Inspired Moduli Stabilization

The simple chaotic inflation is highly consistent with the BICEP2 experiment, and no-scale supergravity can be realized naturally in various string compactifications. Thus, we construct a chaotic inflation model in no-scale supergravity inspired from Type IIB string compactification with an anomalous U(1)_X gauged symmetry. We introduce two moduli T_1 and T_2 which transform non-trivially under U(1)_X, and some pairs of fundamental quarks charged under the SU(N) x U(1)_X gauge group. The non-trivial transformations of moduli under U(1)_X lead to a moduli-dependent Fayet-Iliopoulos (FI) term. The modulus T_2 and the real component of T_1 are stabilized by the non-perturbative effect from quark condensation and the U(1)_X D-term. In particular, the stabilization from the anomalous U(1)_X D-term with moduli-dependent FI term is crucial for inflation since it gives heavy mass to the real component of the modulus T_1 while keeping its axionic part light. Choosing the proper parameters, we obtain a global Minkowski vacuum where the imaginary part of T_1 has a quadratic potential for chaotic inflation.